Siu Long LEI  李兆隆
Associate Professor

Academic Qualifications | Working Experiences | Teaching | Research | Selected Publications | Services | Professional Affiliations | Students | Contact Details

Academic Qualifications
Working Experiences

B.Sc. Courses

  1. Discrete Mathematics (MATB111, MATH1000)
  2. Numerical Analysis (MATB225, MATH2007)

M.Sc. Courses

  1. Numerical Methods for Differential Equations (IMAT009, MATH7009)


  1. Macau Science Award, Second Prize in Natural Science, FDCT Macau, 2018 (with Prof. Haiwei Sun).
  2. Teaching Award, University of Macau, 2004.
  3. The Most Famous Teacher, FST Student Association, University of Macau, 2003.
  4. My Favorite F. S. T. Staff, FST Student Association, University of Macau, 2000.


Research Interests

Recent Research Projects

  1. PI: Lei Siu Long, “Fast algorithms for high-dimensional time-space fractional diffusion equations”. University of Macau. Grant No.: MYRG2018-00025-FST
  2. PI: Lei Siu Long, “A tensor train based fast algorithm for solving high-dimensional fractional partial differential equations”. Science and Technology Development Fund (FDCT) of Macau SAR. Grant No.: 048/2017/A.
  3. PI: Lei Siu Long, “Preconditioning Techniques for High-Dimensional Nonlocal Diffusion Problems”. University of Macau. Grant No.: MYRG2016-00202-FST.
  4. PI: Lei Siu Long, “Splitting Schemes for Fractional Diffusion Equations and Their Fast Algorithms”. Science and Technology Development Fund (FDCT) of Macau SAR. Grant No.: 115/2013/A3.
  5. PI: Lei Siu Long, “Second-order Accurate Numerical Methods for Anomalous Diffusion Problems and Their Fast Algorithms”. University of Macau. Grant No.: MYRG071(Y1-L2)-FST13-LSL.
  6. PI: Lei Siu Long, “Circulant Precoditioners for Fractional Diffusion Equations”. University of Macau. Grant No.: MYRG038(Y1-L1)-FST12-LSL.
  7. PI: Lei Siu Long, “Numerical Methods for Phase-Field Simulation of Two-Phase Flows”. University of Macau. Grant No.: SRG012-FST11-12T-LSL.

Selected Publications

Journal Papers (Name of students is underlined)

  1. X. Chen, D. Ding, S. L. Lei and W. F. Wang, A fast preconditioned iterative method for two-dimensional options pricing under fractional differential models, Computers and Mathematics with Applications, minor revision.
  2. S. L. LeiD. Y. Fan and X. ChenFast solution algorithms for exponentially tempered fractional diffusion equations, Numerical Methods for Partial Differential Equations, 34 (2018), 1301-1323. (link)
  3. S. L. LeiW. F. WangX. Chen and D. Ding, A Fast Preconditioned Penalty Method for American Options Pricing Under Regime-Switching Tempered Fractional Diffusion Models, Journal of Scientific Computing, 75 (2018), 1633-1655. (link)
  4. X. ChenW. F. Wang, D. Ding and S. L. LeiA fast preconditioned policy iteration method for solving the tempered fractional HJB equation governing American options valuation, Computers and Mathematics with Applications, 73 (2017), 1932-1944. (link)
  5. Y. C. Huang and S. L. LeiA fast numerical method for block lower triangular Toeplitz with dense Teoplitz blocks system with applications to time-space fractional diffusion equations, Numerical Algorithms, 76 (2017), 605-616. (link)
  6. L. K. Chou and S. L. LeiFast ADI method for high dimensional fractional diffusion equations in conservative form with preconditioned strategy, Computers and Mathematics with Applications, 73 (2017), 385-403. (link)
  7. W. Qu and S. L. LeiOn CSCS-based iteration method for tempered fractional diffusion equations, Japan Journal of Industrial and Applied Mathematics, 33 (2016), 583-597. (link)
  8. S. L. Lei and Y. C. HuangFast algorithms for high-order numerical methods for space fractional diffusion equations, International Journal of Computer Mathematics, 94 (2017), 1062-1078. (link)
  9. S. L. LeiX. Chen and X. H. ZhangMultilevel circulant preconditioner for high-dimensional fractional diffusion equations, East Asian Journal of Applied Mathematics, 6 (2016), 109-130. (link)
  10. S. W. Vong, P. LyuX. Chen and S. L. LeiHigh order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives, Numerical Algorithms, 72 (2016), 195-210. (link)
  11. Z. B. Wang, S. W. Vong and S. L. LeiFinite difference schemes for two-dimensional time-space fractional differential equations, International Journal of Computer Mathematics, 93 (2016), 578-595. (link)
  12. W. F. WangX. Chen, D. Ding and S. L. LeiCirculant preconditioning technique for barrier options pricing under fractional diffusion models, International Journal of Computer Mathematics, 92 (2015), 2596-2614. (link)
  13. W. QuS. L. Lei and S. W. Vong, A note on the stability of a second order finite difference scheme for space fractional diffusion equations, Numerical Algebra, Control and Optimization, 4 (2014), 317-325. (link)
  14. W. QuS. L. Lei and S. W. Vong, Circulant and skew-circulant splitting iteration for fractional advection-diffusion equations, International Journal of Computer Mathematics, 91 (2014), 2232-2242. (link)
  15. S. L. Lei and H. W. Sun, A circulant preconditioner for fractional diffusion equations, Journal of Computational Physics, 242 (2013), 715-725. (link)
  16. S. W. Vong, Q. J. Meng, and S. L. LeiOn a discrete-time collocation method for the nonlinear Schrodinger equation with wave operator, Numerical Methods for Partial Differential Equations, 29 (2013), 693-705. (link)
  17. S. L. Lei and X. P. Wang, Dripping and jetting in coflowing liquid streams, Advances in Adaptive Data Analysis, 3 (2011), 269-290. (link)
  18. S. L. LeiAdaptive method for spike solutions of Gierer-Meinhardt system on irregular domain, Discrete and Continuous Dynamical Systems - Series B, 15 (2011), 651-668. (link)
  19. C. M. Wu, S. L. Lei, T. Z. Qian and X. P. Wang, Stick-slip motion of moving contact line on chemically patterned surfaces, Communications in Computational Physics, 7 (2010), 403-422. (link)
  20. T. Z. Qian, C. M. Wu, S. L. Lei, X. P. Wang and P. Sheng, Modeling and simulations for molecular scale hydrodynamics of moving contact line in immiscible two-phase flows, Journal of Physics: Condensed Matter, 21 (2009), 464119. (link)
  21. X. Q. Jin, S. L. Lei and Y. M. Wei, Circulant preconditioners for solving singular perturbation delay differential equations, Numerical Linear Algebra with Applications, 12 (2005), 327-336. (link)
  22. X. Q. Jin, S. L. Lei and Y. M. Wei, Circulant preconditioners for solving differential equations with multi-delays, Computers and Mathematics with Applications, 47 (2004), 1429-1436. (link)
  23. S. L. Lei and X. Q. Jin, BCCB preconditioners for systems of BVM-based numerical integrators, Numerical Linear Algebra with Applications, 11 (2004), 25-40. (link)
  24. X. Q. Jin and S. L. LeiSine transform based preconditioners for solving constant-coefficient first-order PDEs, Linear Algebra and its Applications, 366 (2003), 283-294. (link)
  25. F. R. Lin, X. Q. Jin and S. L. LeiStrang-type preconditioners for solving linear systems from delay differential equations, BIT, 43 (2003), 136-149. (link)
  26. S. L. Lei, K. I. Kou and X. Q. Jin, Preconditioners for ill-conditioned block Toeplitz systems with application in image restoration, East-West Journal of Numerical Mathematics, 7 (1999), 175-185. (The journal now is named as Journal of Numerical Mathematics.)

Invited Editor of Special Issue

  1. G. H. Hu, S. L. Lei, and S. W. VongSpecial issue for the 2017 workshop on computational mathematics and scientific computing, Numerical Mathematics: Theory, Methods and Applications, vol. 11 no. (2018).
  2. G. H. Hu, S. L. Lei, and S. W. Vong, Special issue for the EASIAM annual conference 2016, East Asian Journal on Applied Mathematics, vol. 7 no. 4 (2017)
  3. G. H. Hu, S. L. Lei, and S. W. Vong, Special issue for the fourth workshop on numerical algebra and high performance computation, East Asian Journal on Applied Mathematics, vol. no. 1 (2014).

Conference Papers

  1. S. L. Lei, M. Lao and I. Chan, Simulation on vortex effect for superconducting devices, Computational Methods in Engineering and Science - Proceedings of EPMESC X (2006), pp. 313-318. Eds: Z. Yao, M. Yuan and Y. Chen, Tsinghua University Press and Springer, 2006.
  2. S. L. Lei and X. Q. Jin, Strang-type preconditioners for solving differential-algebraic equations, NAA (2000), Lecture Notes in Computer Science, Vol. 1988, pp. 505-512, Eds.: L. Vulkov, J. Wasniewski and P. Yalamov, Springer, 2001.


Professional Services

University Services

Community Services

Professional Affiliations

Master Students

PhD Student

Contact Details

Faculty of Science and Technology
University of Macau, E11
Avenida da Universidade, Taipa,
Macau, China

Room: E11-3066
Telephone: (853) 8822-4449
Fax: (853) 8822-2426
Email: sllei